A marketing company surveyed 2500 potential customers about their preferences for a new smartphone model. The options for features are classified by: screen size (Large or Standard), camera quality (High or Medium), and operating system (Android or iOS). You are given the following information:

• 1400 customers prefer a Large screen size.
• 1300 customers prefer High camera quality.
• 1100 customers prefer iOS.
• 600 customers prefer a Large screen and Medium camera quality.
• 700 customers prefer a Large screen and Android.
• 750 customers prefer Android and High camera quality.
• 400 customers prefer a Standard screen, Medium camera quality, and Android.

Determine the number of customers who prefer a Standard screen, High camera quality, and iOS.

• 150
• 200
• 250
• 300
• 350

A university conducted a survey among its students to understand their engagement in extracurricular activities. They focused on participation in sports clubs and academic societies. You are given the following probabilities:

• The probability that a randomly selected student participates in a sports club is 60%.
• The probability that a randomly selected student participates in an academic society is 45%.
• The probability that a randomly selected student participates in at least one of these (either a sports club or an academic society, or both) is 80%.

Determine the probability that a randomly selected student participates in a sports club but does not participate in an academic society.

• 0.25
• 0.30
• 0.35
• 0.40
• 0.45

A university is introducing three new optional workshops for its incoming freshmen: "Study Skills (SS)", "Career Planning (CP)", and "Financial Literacy (FL)". Students are encouraged to enroll in Study Skills. However, due to scheduling constraints and content overlap, students can only choose one of Career Planning or Financial Literacy, not both. The university compiled the following enrollment statistics:

• 12% of freshmen chose not to enroll in any workshop.
• 75% of freshmen enrolled for Study Skills coverage.
• 40% of freshmen enrolled for Study Skills but not Financial Literacy.
• 8% of freshmen enrolled for Career Planning but not Study Skills.

Determine the percentage of freshmen who enrolled in Financial Literacy.

• 32%
• 36%
• 40%
• 44%
• 48%

A survey of households in a city reveals the following about pet ownership:

• The probability that a randomly chosen household owns a cat but not a dog is twice the probability that it owns both a cat and a dog.
• The probability that a randomly chosen household owns a dog but not a cat is three times the probability that it owns both a cat and a dog.
• The probability that a randomly chosen household owns at least one of these two types of pets (cat or dog) is 60%.

Let [math]A[/math] be the event that a household owns a cat, and [math]B[/math] be the event that a household owns a dog. Determine [math]\operatorname{P}(A)[/math].

• 0.1
• 0.2
• 0.3
• 0.4
• 0.5

Suppose a company manufactures electronic devices, and each device can have three types of defects: Cosmetic (A), Functional (B), and Software (C). For a particular batch of devices, the probabilities of these defects follow these rules:

• The probability that a device has either a Cosmetic or a Functional defect is [math]\frac{4}{5}[/math] of the sum of the probabilities of having a Cosmetic defect and having a Functional defect individually.
• The probability of a Cosmetic defect is twice the probability of a Functional defect.
• The probability of a Functional defect is three times the probability of a Software defect.
• Every device in this batch has at least one of these three types of defects.
• A device with a Software defect never has a Cosmetic or Functional defect.

Determine the probability that a device has a functional defect but no cosmetic defect.

• 0
• 1/41
• 6/41
• 9/41
• 15/41

A university advisor is analyzing student data to understand engagement and academic success. A random student is selected.

• The probability that the student participates in extracurricular activities is 65%.
• The probability that the student does not achieve a GPA of 3.5 or higher is 40%.
• The probability that the student either participates in extracurricular activities or achieves a GPA of 3.5 or higher (or both) is 85%.

Determine the probability that a randomly selected student achieves a GPA of 3.5 or higher but does not participate in extracurricular activities.

• 0.15
• 0.20
• 0.25
• 0.40
• 0.60

A recent survey was conducted among college students regarding their regular use of mobile applications. It was found that 20% of students regularly use both social media apps and productivity apps. The survey also revealed that 65% of students do not regularly use either social media apps nor productivity apps. Determine the percentage of college students who regularly use either social media apps or productivity apps, but not both.

• 0.1
• 0.15
• 0.2
• 0.25
• 0.35

A university advisor is analyzing student data to understand engagement and academic success. A random student is selected.

• The probability that the student participates in extracurricular activities is 65%.
• The probability that the student does not achieve a GPA of 3.5 or higher is 40%.
• The probability that the student either participates in extracurricular activities or achieves a GPA of 3.5 or higher (or both) is 85%.

Determine the probability that a randomly selected student achieves a GPA of 3.5 or higher but does not participate in extracurricular activities.

• 0.15
• 0.20
• 0.25
• 0.40
• 0.60

A survey of households in a city reveals the following about pet ownership:

• The probability that a randomly chosen household owns a cat but not a dog is twice the probability that it owns both a cat and a dog.
• The probability that a randomly chosen household owns a dog but not a cat is three times the probability that it owns both a cat and a dog.
• The probability that a randomly chosen household owns at least one of these two types of pets (cat or dog) is 60%.

Let [math]A[/math] be the event that a household owns a cat, and [math]B[/math] be the event that a household owns a dog. Determine [math]\operatorname{P}(A)[/math].

• 0.1
• 0.2
• 0.3
• 0.4
• 0.5

A marketing team is analyzing customer purchase patterns for three products: Product X (event [math]A[/math]), Product Y (event [math]B[/math]), and Product Z (event [math]C[/math]). They have gathered the following statistics:

• The probability that a customer purchases both Product X and Product Y is [math]20\%[/math] of the probability that they purchase Product X.
• The probability of purchasing Product Y is twice the probability of purchasing Product X.
• The probability of purchasing Product Z is half the probability of purchasing Product X.
• Customers who purchase Product Z never purchase Product X or Product Y.
• The probability that a customer purchases at least one of the three products is [math]90\%[/math].

Determine the probability that a customer purchases Product Y but not Product X.

• 3/55
• 6/11
• 27/55
• 3/11
• 12/55